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Chloé Winters
STA 551
Fall 2025
Introduction
Methodology & Analysis
Results & Conclusion
General Discussion
Customer churn represents a loss of revenue and increased acquisition costs.
Understanding what drives churn drivers allows for targeted retention.
This assignment will compare models and determining the optimal one
Three logistic models were evaluated:
Full model
Reduced model
Stepwise-selected model
Models were compared using ROC curves and AUC on a held-out test set.
| Predictor | Odds Ratio | p-value |
|---|---|---|
| (Intercept) | 1.410 | 0.751 |
| SexMale | 0.941 | 0.777 |
| MaritalStatusSingle | 1.022 | 0.961 |
| Term | 0.927 | 0.000 |
| PhoneserviceYes | 1.005 | 0.994 |
| InternationalplanYes | 1.106 | 0.700 |
| VoicemailplanYes | 0.852 | 0.463 |
| MultiplelineNo phone | NA | NA |
| MultiplelineYes | 0.853 | 0.543 |
| InternetserviceDSL | 0.588 | 0.261 |
| InternetserviceFiber optic | 0.843 | 0.538 |
| InternetserviceNo Internet | 0.145 | 0.038 |
| TechnicalsupportNo internet | NA | NA |
| TechnicalsupportYes | 0.665 | 0.142 |
| StreamingVideosNo internet | NA | NA |
| StreamingVideosYes | 1.365 | 0.369 |
| AgreementperiodOne year contract | 0.200 | 0.000 |
| AgreementperiodTwo year contract | 0.119 | 0.000 |
| MonthlyCharges | 1.003 | 0.857 |
| TotalCharges | 1.001 | 0.003 |
| Predictor | Odds Ratio | p-value |
|---|---|---|
| (Intercept) | 1.630 | 0.061 |
| Term | 0.926 | 0.000 |
| InternetserviceDSL | 0.556 | 0.065 |
| InternetserviceFiber optic | 0.894 | 0.671 |
| InternetserviceNo Internet | 0.129 | 0.000 |
| AgreementperiodOne year contract | 0.181 | 0.000 |
| AgreementperiodTwo year contract | 0.101 | 0.000 |
| TotalCharges | 1.001 | 0.000 |
| Predictor | Odds Ratio | p-value |
|---|---|---|
| (Intercept) | 0.606 | 0.319 |
| Term | 0.927 | 0.000 |
| TechnicalsupportNo internet | 0.270 | 0.011 |
| TechnicalsupportYes | 0.637 | 0.080 |
| AgreementperiodOne year contract | 0.200 | 0.000 |
| AgreementperiodTwo year contract | 0.117 | 0.000 |
| MonthlyCharges | 1.012 | 0.079 |
| TotalCharges | 1.001 | 0.003 |
| Metric | Value |
|---|---|
| error | 0.0126 |
| reached.threshold | 0.0095 |
| steps | 100.0000 |
| Intercept.to.1layhid1 | -1.5170 |
| SexFemale.to.1layhid1 | -0.5295 |
| SexMale.to.1layhid1 | -0.6308 |
| MaritalStatusSingle.to.1layhid1 | -0.2157 |
| PhoneserviceYes.to.1layhid1 | -1.9458 |
| InternationalplanYes.to.1layhid1 | -0.3901 |
| VoicemailplanYes.to.1layhid1 | -0.2306 |
| MultiplelineNo.phone..to.1layhid1 | -2.2922 |
| MultiplelineYes.to.1layhid1 | -0.0478 |
| InternetserviceDSL.to.1layhid1 | -0.4440 |
| InternetserviceFiber.optic.to.1layhid1 | -0.3280 |
| InternetserviceNo.Internet.to.1layhid1 | -0.8579 |
| TechnicalsupportNo.internet..to.1layhid1 | -0.6097 |
| TechnicalsupportYes.to.1layhid1 | -0.1890 |
| StreamingVideosNo.internet..to.1layhid1 | 0.6980 |
| StreamingVideosYes.to.1layhid1 | -0.0192 |
| AgreementperiodOne.year.contract.to.1layhid1 | -0.5605 |
| AgreementperiodTwo.year.contract.to.1layhid1 | -0.4707 |
| ChurnYes.to.1layhid1 | 10.8148 |
| Termscale.to.1layhid1 | -1.3392 |
| MonthlyChargesscale.to.1layhid1 | 0.5239 |
| TotalChargesscale.to.1layhid1 | 0.0469 |
| Intercept.to.Churnnum | -5.2526 |
| 1layhid1.to.Churnnum | 10.1725 |
| Metric | Value |
|---|---|
| error | 49.5837 |
| reached.threshold | 0.0086 |
| steps | 2002.0000 |
| Intercept.to.1layhid1 | -0.2363 |
| Termscale.to.1layhid1 | 5.9524 |
| TotalChargesscale.to.1layhid1 | -7.0861 |
| AgreementperiodOne.year.contract.to.1layhid1 | 1.2362 |
| AgreementperiodTwo.year.contract.to.1layhid1 | 2.5294 |
| Intercept.to.Churnnum | 3.1122 |
| 1layhid1.to.Churnnum | -6.8599 |
Model AUC 1 Full Logistic 0.8042817 2
Reduced Logistic 0.7915127 3 Stepwise Logistic 0.8081395
Model AUC 1 Full Perceptron 1.0000000 2 Reduced Perceptron
0.7410074
Final optimal model is the stepwise logistic regression
Due to the smaller AUC and more stability
Good amount of variable overlap with other models
[ \text{Churn} = -0.5002 - 0.0758(\text{Term}) - 1.309(\text{TSNoInternet}) - 0.451(\text{TSYes}) \ - 1.612(\text{OneYear}) - 2.146(\text{TwoYear}) \ + 0.01183(\text{MonthlyCharges}) + 0.000642(\text{TotalCharges}) ]
Potential faults
Stepwise model might be harder to interpret to non statisticians
If someone does not understand how to implement a model its useless to them
Questions?